If you are moving this data into a different FileMaker file, don't export any data. Instead, import the data from the other FileMaker file directly. This method can import container field data just like any other field type.
IF you must export data into a file such as csv, tab, merge, or excel, these file formats cannot support data from container fields and thus you cannot export the contents of a container field into such a file. But data in container fields are themselves files. You can use export field contents to export the data from container fields to produce a set of files along with the data file produced by export records.
Since export field contents exports data from a single field, you'll want to use a script to export this data if you have to export the data in this fashion.